Quantitative Traits

Preliminaries

If you are already familiar with the structure of these exercises, read the Introduction first.

Note

Reminder: Save your work regularly.

Important

If you are using a Mac, we recommend that you use either Chrome or Firefox to complete these exercises. Some of the default settings in Safari prevent these exercises from running.

Contact information

If you have questions about these exercises, please contact Dr. Kevin Middleton (middletonk@missouri.edu) or drop by Tucker 224.

Learning Objectives

The learning objectives for this exercise are:

Explain how polygenic traits differ from Mendelian traits
Explain how traits with continuous (also called quantitative) phenotypic measures result from the combined effects of many different genes
Describe how many genes can each contribute a small amount to a phenotype
Explain what quantitative trait loci (QTL) are and how QTL are discovered
Explain how the contributions of many genes of small effect can be associated with a disease or condition

Contrasting Mendelian traits and polygenic traits

Dominant/recessive to just thinking about alternate alleles (major vs. minor)

What are quantitative traits?

Counting the ways: Binomial Coefficent

Continuous traits from combinations of many Mendelian traits

Combinations of alleles are binomial

Large numbers of small additions and subtractions are normal

Make some assumptions:

Additivity can mean adding negative numbers
All genes have roughly equal effect
Gene do not interact with one another

Case study: QTL mapping

Shapiro pigeon example (dominant trait)

Figure 1: FIXME Image from (Shapiro et al. 2013)

Figure 2: FIXME Image from (Shapiro et al. 2013)

Case study: Human height

(Visscher et al. 2012)

Best understood quantitative trait in humans
Yet still 700 genes

(Visscher et al. 2017)

Yengo et al. (2018):

~700,000 individuals
3290 (“near-independent”) SNPs explain ~25% of the variation in human height among Europeans
Estimated to be ~700 explaining ~16% of variation in 2010 (Lango Allen et al. 2010)

NH <- readRDS("NHANES/NHANES.Rds")

The National Health and Nutrition Examination Survey (“NHANES”) began in the early 1960’s and continues to this day. The goal is to assess the health and nutrition status of a broad cross-section of the population. As part of this study, height (in cm) and body mass (in kg) are recorded for each participant.

Data from the 2017-2020 NHANES survey has data for 13137

NH |> 
  group_by(Sex) |> 
  summarize(across(.cols = everything(), list(mean = mean, sd = sd)))

# A tibble: 2 × 7
  Sex       Age_mean Age_sd Weight_mean Weight_sd Height_mean Height_sd
  <chr>        <dbl>  <dbl>       <dbl>     <dbl>       <dbl>     <dbl>
1 XX Female     36.1   24.0        66.1      29.3        152.      19.7
2 XY Male       35.9   24.5        72.6      32.1        161.      24.3

ggplot(NH, aes(Height, fill = Sex)) +
  geom_histogram(bins = 30, show.legend = FALSE) +
  scale_fill_manual(values = c("goldenrod", "firebrick")) +
  facet_grid(Sex ~ .) +
  labs(x = "Height (cm)", y = "Count")

Threshold traits

Schizophrenia (~200 genes)

Why family history is one of the most important diagnostic tools in medicine

References

Lango Allen, H., K. Estrada, G. Lettre, S. I. Berndt, M. N. Weedon, F. Rivadeneira, C. J. Willer, A. U. Jackson, S. Vedantam, S. Raychaudhuri, T. Ferreira, A. R. Wood, R. J. Weyant, A. V. Segrè, E. K. Speliotes, E. Wheeler, N. Soranzo, J.-H. Park, J. Yang, D. Gudbjartsson, N. L. Heard-Costa, J. C. Randall, L. Qi, A. Vernon Smith, R. Mägi, T. Pastinen, L. Liang, I. M. Heid, J. Luan, G. Thorleifsson, T. W. Winkler, M. E. Goddard, K. Sin Lo, C. Palmer, T. Workalemahu, Y. S. Aulchenko, A. Johansson, M. C. Zillikens, M. F. Feitosa, T. Esko, T. Johnson, S. Ketkar, P. Kraft, M. Mangino, I. Prokopenko, D. Absher, E. Albrecht, F. Ernst, N. L. Glazer, C. Hayward, J.-J. Hottenga, K. B. Jacobs, J. W. Knowles, Z. Kutalik, K. L. Monda, O. Polasek, M. Preuss, N. W. Rayner, N. R. Robertson, V. Steinthorsdottir, J. P. Tyrer, B. F. Voight, F. Wiklund, J. Xu, J. H. Zhao, D. R. Nyholt, N. Pellikka, M. Perola, J. R. B. Perry, I. Surakka, M.-L. Tammesoo, E. L. Altmaier, N. Amin, T. Aspelund, T. Bhangale, G. Boucher, D. I. Chasman, C. Chen, L. Coin, M. N. Cooper, A. L. Dixon, Q. Gibson, E. Grundberg, K. Hao, M. Juhani Junttila, L. M. Kaplan, J. Kettunen, I. R. König, T. Kwan, R. W. Lawrence, D. F. Levinson, M. Lorentzon, B. McKnight, A. P. Morris, M. Müller, J. Suh Ngwa, S. Purcell, S. Rafelt, R. M. Salem, E. Salvi, S. Sanna, J. Shi, U. Sovio, J. R. Thompson, M. C. Turchin, L. Vandenput, D. J. Verlaan, V. Vitart, C. C. White, A. Ziegler, P. Almgren, A. J. Balmforth, H. Campbell, L. Citterio, A. De Grandi, A. Dominiczak, J. Duan, P. Elliott, R. Elosua, J. G. Eriksson, N. B. Freimer, E. J. C. Geus, N. Glorioso, S. Haiqing, A.-L. Hartikainen, A. S. Havulinna, A. A. Hicks, J. Hui, W. Igl, T. Illig, A. Jula, E. Kajantie, T. O. Kilpeläinen, M. Koiranen, I. Kolcic, S. Koskinen, P. Kovacs, J. Laitinen, J. Liu, M.-L. Lokki, A. Marusic, A. Maschio, T. Meitinger, A. Mulas, G. Paré, A. N. Parker, J. F. Peden, A. Petersmann, I. Pichler, K. H. Pietiläinen, A. Pouta, M. Ridderstråle, J. I. Rotter, J. G. Sambrook, A. R. Sanders, C. O. Schmidt, J. Sinisalo, J. H. Smit, H. M. Stringham, G. Bragi Walters, E. Widen, S. H. Wild, G. Willemsen, L. Zagato, L. Zgaga, P. Zitting, H. Alavere, M. Farrall, W. L. McArdle, M. Nelis, M. J. Peters, S. Ripatti, J. B. J. van Meurs, K. K. Aben, K. G. Ardlie, J. S. Beckmann, J. P. Beilby, R. N. Bergman, S. Bergmann, F. S. Collins, D. Cusi, M. den Heijer, G. Eiriksdottir, P. V. Gejman, A. S. Hall, A. Hamsten, H. V. Huikuri, C. Iribarren, M. Kähönen, J. Kaprio, S. Kathiresan, L. Kiemeney, T. Kocher, L. J. Launer, T. Lehtimäki, O. Melander, T. H. Mosley Jr, A. W. Musk, M. S. Nieminen, C. J. O’Donnell, C. Ohlsson, B. Oostra, L. J. Palmer, O. Raitakari, P. M. Ridker, J. D. Rioux, A. Rissanen, C. Rivolta, H. Schunkert, A. R. Shuldiner, D. S. Siscovick, M. Stumvoll, A. Tönjes, J. Tuomilehto, G.-J. van Ommen, J. Viikari, A. C. Heath, N. G. Martin, G. W. Montgomery, M. A. Province, M. Kayser, A. M. Arnold, L. D. Atwood, E. Boerwinkle, S. J. Chanock, P. Deloukas, C. Gieger, H. Grönberg, P. Hall, A. T. Hattersley, C. Hengstenberg, W. Hoffman, G. M. Lathrop, V. Salomaa, S. Schreiber, M. Uda, D. Waterworth, A. F. Wright, T. L. Assimes, I. Barroso, A. Hofman, K. L. Mohlke, D. I. Boomsma, M. J. Caulfield, L. A. Cupples, J. Erdmann, C. S. Fox, V. Gudnason, U. Gyllensten, T. B. Harris, R. B. Hayes, M.-R. Jarvelin, V. Mooser, P. B. Munroe, W. H. Ouwehand, B. W. Penninx, P. P. Pramstaller, T. Quertermous, I. Rudan, N. J. Samani, T. D. Spector, H. Völzke, H. Watkins, J. F. Wilson, L. C. Groop, T. Haritunians, F. B. Hu, R. C. Kaplan, A. Metspalu, K. E. North, D. Schlessinger, N. J. Wareham, D. J. Hunter, J. R. O’Connell, D. P. Strachan, H.-E. Wichmann, I. B. Borecki, C. M. van Duijn, E. E. Schadt, U. Thorsteinsdottir, L. Peltonen, A. G. Uitterlinden, P. M. Visscher, N. Chatterjee, R. J. F. Loos, M. Boehnke, M. I. McCarthy, E. Ingelsson, C. M. Lindgren, G. R. Abecasis, K. Stefansson, T. M. Frayling, and J. N. Hirschhorn. 2010. Hundreds of Variants Clustered in Genomic Loci and Biological Pathways Affect Human Height. Nature 467:832–838.

Shapiro, M. D., Z. Kronenberg, C. Li, E. T. Domyan, H. Pan, M. Campbell, H. Tan, C. D. Huff, H. Hu, A. I. Vickrey, S. C. A. Nielsen, S. A. Stringham, H. Hu, E. Willerslev, M. T. P. Gilbert, M. Yandell, G. Zhang, and J. Wang. 2013. Genomic Diversity and Evolution of the Head Crest in the Rock Pigeon. Science, doi: 10.1126/science.1230422.

Visscher, P. M., M. A. Brown, M. I. McCarthy, and J. Yang. 2012. Five Years of GWAS Discovery. Am. J. Hum. Genet. 90:7–24. cell.com.

Visscher, P. M., N. R. Wray, Q. Zhang, P. Sklar, M. I. McCarthy, M. A. Brown, and J. Yang. 2017. 10 Years of GWAS Discovery: Biology, Function, and Translation. Am. J. Hum. Genet. 101:5–22.

Yengo, L., J. Sidorenko, K. E. Kemper, Z. Zheng, A. R. Wood, M. N. Weedon, T. M. Frayling, J. Hirschhorn, J. Yang, P. M. Visscher, and GIANT Consortium. 2018. Meta-Analysis of Genome-Wide Association Studies for Height and Body Mass Index in ∼700000 Individuals of European Ancestry. Hum. Mol. Genet. 27:3641–3649. Oxford University Press (OUP).